What does the referring expression “peggy’s dress is green” presuppose?

This expression presupposes that the hearer of the expression knows who Peggy is.

A referring expression presupposes that the hearer of the expression recognizes the speaker's intention. Therefore, the speaker assumes the hearer knows who Peggy is.

It explains why the system is now a protected national park.

Explanation:

In the text above we can see that the author explains that there is a need to protect the remains of the human population that live in the caves. he claims that this protection happens because these remains are very old and therefore very fragile and can be easily damaged, but their preservation is important because they are artifacts of human life. This explanation serves to show the reason why the cave system was transformed into a protected park.